Question #24008

• The value of m for which 2x+3y=11 , y=mx+3 , 2x-4y=-24 has common solution is?

Expert's answer

First, we find the solution for (1) 2x+3y=11

(2) 2x-4y=-24

(1) - (2):

2x-2x+3y-(-4y) = 35 => 7y=35

y=5

From the first:

2x+3*5=11 => 2x=-4

x=-2

Therefore y=mx+3 also has solution (-2, 5)

5=m*(-2) +3

m=-1

Answer: m=-1.

(2) 2x-4y=-24

(1) - (2):

2x-2x+3y-(-4y) = 35 => 7y=35

y=5

From the first:

2x+3*5=11 => 2x=-4

x=-2

Therefore y=mx+3 also has solution (-2, 5)

5=m*(-2) +3

m=-1

Answer: m=-1.

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